ODE
\[ y''(x)+8 y'(x)+16 y(x)=4 e^x-e^{2 x} \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.227772 (sec), leaf count = 35
\[\left \{\left \{y(x)\to \frac {4 e^x}{25}-\frac {e^{2 x}}{36}+e^{-4 x} (c_2 x+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.066 (sec), leaf count = 28
\[\left [y \left (x \right ) = {\mathrm e}^{-4 x} \textit {\_C2} +{\mathrm e}^{-4 x} x \textit {\_C1} +\frac {4 \,{\mathrm e}^{x}}{25}-\frac {{\mathrm e}^{2 x}}{36}\right ]\] Mathematica raw input
DSolve[16*y[x] + 8*y'[x] + y''[x] == 4*E^x - E^(2*x),y[x],x]
Mathematica raw output
{{y[x] -> (4*E^x)/25 - E^(2*x)/36 + (C[1] + x*C[2])/E^(4*x)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+8*diff(y(x),x)+16*y(x) = 4*exp(x)-exp(2*x), y(x))
Maple raw output
[y(x) = exp(-4*x)*_C2+exp(-4*x)*x*_C1+4/25*exp(x)-1/36*exp(2*x)]